Rashid Akmaev, a research scientist at the University of Colorado, explains.
The short answer is yes, and at various times this question of lunar
tides in the atmosphere occupied such famous scientists as Isaac Newton
and Pierre-Simon Laplace, among others. Newton's theory of gravity
provided the first correct explanation of ocean tides and their long
known correlation with the phases of the moon. Roughly a century later
it was also used to predict the existence of atmospheric tides when
Laplace developed a quantitative theory based on a tidal equation now
bearing his name. Laplace's equation describes the motions of an ocean
of uniform depth covering a spherical Earth [see illustration].
At the point on the ocean's surface closest to the moon (point A
in the illustration), the lunar gravitational attractive force is
strongest and it pulls the ocean toward itself. On the opposite side of
Earth (point B), its attractive force is weakest, which allows the ocean
to bulge outward again, in this case away from the moon. As the planet
rotates from west to east the two bulges tend to stay on the Earth-moon
line. (The moon also revolves around Earth in the same direction as
Earth's rotation but at a much slower rate.) For an observer stationed
on the surface and revolving with it, the bulges would appear as a giant
wave, which follows the apparent motion of the moon to the west and has
two crests per lunar day.
https://www.scientificamerican.com/article/does-the-moon-have-a-tida/
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